Mirabilis ICQ 2000 includes an option in the ICQ, Security & Privacy dialog box (Ignore tab) to prevent direct connection with old versions of ICQ. Miranda is treated as an old version, so cannot directly communicate with ICQ clients that have this setting switched on.
Before version 4.65, build #3281 (see ICQ, Help, About), this setting was off by default, however after that, this setting was switched on at installation, even if you had previously switched it off.
There are two solutions to this problem: the ideal one is to persuade your friend to switch off that setting (noting that Mirabilis ICQ must be restarted for the change to take effect); the other is to send all messages through the server, however this is slower and you can only send a maximum of 450 characters in a message.
Miranda contains logic to work around users who have this setting on. If enabled, it will shorten the send timeout for messages to 2 seconds, and if this fails, it will automatically retry sending the current message, and all future messages for this session, through the server. If Miranda manages to send the message direct in 2 seconds, it will assume that the user can now accept direct connections and revert to the normal logic for all future communications.